Study of Bank’s Optimal Loan-to-value Ratios Impacted by Liquidation Delay and Liquidity Risk in Environment with Uncertainty

Hui ZHANG, Wen-feng DI, Yuan-yuan LU


We consider the inventory financing commodities such as copper and aluminum with short-term price following geometric Brownian motion. We take the research of the small and medium enterprises’ default probability impacted by such factors as the price volatility, the liquidation delay and the liquidity risk of the collateral. We establish the maximum and minimum levels of risk tolerance as the bank's maximum and minimum risk preferences in environment with Knightian uncertainty. We build the models about the loan-to-value ratios with the bank's maximum and minimum risk preferences. And we give the explicit solutions of models about the LTVratios. Finally, we get the numerical solutions of models.


Loan-to-value (LTV) ratios, Risk preference, Liquidation delay, Liquidity risk


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